# At a Glance - Continuity at a Point

Continuity is easiest if we begin by thinking of it at a single point. Once we have that down we can start thinking of continuity in broader terms. There's a couple conditions that have to be met for us to say a function is continuous at a point *c*.

The first condition is that *f*(*c*) has to actually exist. We can't have a hole in the graph at *c*, or an asymptote, or anything that's going to make *f*(*c*) not exist as a nice, real number.

In other words, *c* has to be in the domain of *f*.

This isn't the only condition, though. We also need

.

If these two conditions are met, we say that *f* is **continuous** at *x* = *c*.

In words, the function doesn't jump around at *x* = *c*. There will be no surprises; the function will pass smoothly through *x* = *c* unscathed. The limit as we approach *c* will exist and be equal *f*(*c*).